I'd really love Locke to be a floatier, speedier character to play that has a movement style more evocative of Quake than Halo. Him darting around, making huge leaps, slowly but surely dancing around perimeters and taking down targets one by one. You could chalk it up to him having integrated Forerunner tech or even show that he has retro-rockets built into his suit's extremities that allow him to have extremely long leaps and strafes without having a ton of baggage in terms of momentum, which would give him a much tighter movement style in general. With all of his permissions in-universe, I'd expect Locke to actually have a more arena shooter sort of style rather than making his missions the "modern-feeling" ones. Playing as Buck in Spartan-IV mode would probably be a better way to do a "modern" campaign with Sprint, ADS, etc. Locke could have something like a drastically shortened recharge timer on his Thrusters and Sprint replaced with a general "grinding" mechanic that sends him shooting across walls, rails, etc.
By relative contrast, Chief would have a more "sluggish" moveset fueled by mass and momentum, but his attacks would have a little more oomph by proxy - he'd have to commit to the moves he makes. I think it'd make for a great establishing character moment if Chief and Locke have to briefly square off early on, and while Chief keeps trying to stick to his guns (literally, as in AR, BR, whatever) Locke's combat style is way too aggressive and he keeps closing distance, so Chief prepares to for CQC only to be immediately outclassed. Locke's fisticuffs are equal parts acrobatic and pragmatic and he starts throwing off sucker punches, roundhouse kicks fueled by retro rockets, etc. At some point during a kick Chief manages to get a hold on Locke's leg and tries to suplex him / throw him to the ground only for Locke to immediately pivot, thrust to right himself and knees Chief in the face. Maybe Chief and Locke having an early fight is what's responsible for the damage to Chief's armor, only for him to escape somehow. All of Locke's shiny new ONI toys could similarly be used to scare Chief into thinking he's outmoded - Locke going "You're getting slow on me, Chief! You've got to keep up!" or something similar.